The page style for the first page of a chapter is set internally (in the book and report document classes) to be plain; you can change this behaviour by adding the following lines to the preamble of your document:
\makeatletter
\renewcommand\chapter{\if@openright\cleardoublepage\else\clearpage\fi
\thispagestyle{empty}% original style: plain
\global\@topnum\z@
\@afterindentfalse
\secdef\@chapter\@schapter}
\makeatother
or, using the etoolbox package:
\usepackage{etoolbox}
\patchcmd{\chapter}{plain}{empty}{}{}
If the plain style is not needed elsewhere, then you can redefine it to be the empty page style; this can be done with:
\makeatletter
\let\ps@plain\ps@empty
\makeatother
Finally, in the scrbook document class (from the KOMA-Script bundle), the style for the first page of chapters can be changed simply by redefining the \chapterpagestyle command, as in:
\renewcommand*\chapterpagestyle{empty}
EDIT: added egreg's remarks.